ACCEPT their request (which must be for incorrect dates that ARE open on your calendar, right?) and state:
“I am accepting your INQUIRY [or sending you a special offer] in keeping with AirBNB’s metrics to evaluate us hosts, but please don’t book unless you really wish to visit on dates open on my calendar.”
In other words – make it LOOK (at Air’s end) like you are accepting everyone.
OR try to sell your open weeks to guests who inquire. Or offer them the random 4 days they want at full price. Keep the ball rolling with creative offers that benefit you and your setup – note to guests this is a rare opportunity for your seasonal listing.
OH WAIT: This assumes that you are syncing your calendars or manually blocking off the Air dates that aren’t available as TheInsider notes. I read now that you are doing manual updates.